Assume we have k immediate (due)-annuities with different interest rates. Let i=(i1,i2,...,ik) and i∗=(i∗1,i∗2,...,i∗k) be two vectors of interest rates such that i∗ is majorized by i. It's shown that sum of present and accumulated value of annuities-immediate with interest rate i is grater than sum of present value of annuities-immediate with interest rate i∗. We also prove the similar results for annuities-due.
